Statistics VI - PCA + Meta Exam Questions + Vectors/Matrices Flashcards Preview

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Flashcards in Statistics VI - PCA + Meta Exam Questions + Vectors/Matrices Deck (31)
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1
Q

What should the PCA be based on if all variables have the same units?

A

the covariance matrix

2
Q

What should the PCA be based on if variables have different units?

A

the correlation matrix

3
Q

In a PCA of a bivariate distributions: The coordination system is rotated so that …

A

… the first axis - the first PC - has the largest possible variance.

4
Q

How come we are allowed to rotate the coordination system in the PCA?

A

We are allowed to do that, because the total variance is invariant against rotation of data.

5
Q

The sum of squared distances of a distribution = 3.224.

What is the sum of squared distances after rotating the data in the course of a PCA?

A

the same: 3.224

6
Q

The second PC has the ___________ largest variance and is _________ to the first PC.

A

The second PC has the SECOND largest variance and is ORTHOGONAL to the first PC.

7
Q

What’s the total variance in the following (graphically akward) covariance matrix?
[0.950 0.647]
[0.647 0.820]

A

0.950 + 0.820 = 1.770

8
Q

What multivariate tests should we know?

A

MANCOVA
MANOVA
Hotelling’s T²

9
Q

What univariate tests should we know?

A

student’s t-test
ANOVA
ANCOVA

10
Q

What is an eigenvector and an eigenvalue?

A

If A is a square matrix, v != 0 is an eigenvector of A, if
A * v = λ * v

The number λ is called the eigenvalue of A.

11
Q

List at least 6 tests!

A
student's t-test
Hotelling's T²
ANOVA
ANCOVA
MANOVA
MANCOVA
12
Q

What can the following tests be useful for:
t-test
ANOVA
ANCOVA

A

t-test: difference btw 2 groups and 1 variable
ANOVA: difference btw several groups, one dependent variable
ANCOVA: difference btw several groups, one dependent variable + controls

13
Q

What can the following tests be useful for:
Hotelling’s T²
MANOVA
MANCOVA

A

Hotelling’s T²: difference btw 2 groups and several variables
MANOVA: several dependent variables, groups, interaction among variables
MANCOVA: several dependent variables, groups, interaction among variables + controls

14
Q

How is the name of a vector usually written in statistics?

A

bold lowercase letter

15
Q

How many columns does a vector have?

A

1

16
Q

What’s the difference between the vector v and the vector v’?

A

v is a column vector and

v’ is the transposed version of vector v

17
Q

In a matrix, what is represented through rows and columns?

A

rows: cases
columns: variables

18
Q

How does M’ look like if M =
(2 4 1)
(3 8 4)

A

(2 3)
(4 8)
(1 4)

19
Q

What’s the distinct property of a square matrix?

A

Same amount of rows and columns.

20
Q

What’s the distinct property of a symmetric matrix?

A

S = S’

21
Q

What’s the (main) diagonal of a matrix?

A

The “row” of numbers from top left to bottom right.

22
Q

What is an identity matrix (aka. unit matrix)?

A

An identity matrix is a square matrix with ones on the main diagonal.

23
Q

Cor(a,b) = 0.8

How large is the explained variance?

A

0.8² = 0.64 -> 64 %

24
Q

Cor(a,b) = - 0.3

How large is the explained variance?

A
  • 0.3² = 0.09 -> 9 %
25
Q

What’s the definition of discrete data?

A

Discrete Data can only take certain values.

26
Q

What’s the definition of continuous data?

A

Continuous Data is data that can take any value (within a range)

27
Q

What kind of a scale is Kelvin?

A

ratio scale

28
Q

What kind of a scale is Celsius?

A

interval scale

29
Q

Define precision!

A

Degree to which repeated measurements show the same results

30
Q

Define accuracy!

A

Closeness of measurements of a quantity to the quantity’s actual (true) value.

31
Q

Define bias!

A

Difference between the average of the measurements and the reference value.